See W. J. Mitchell, Elementary Harmony (3d ed. 1965); A. Schoenberg, Structural Functions of Harmony (rev. ed. 1969); W. Piston, Harmony (5th ed. 1987).
Nevertheless, the simultaneous sounding of notes was not part of musical practice in antiquity; harmonía merely provided a system of classification for the relationships between different pitches. In the Middle Ages the term was used to describe two pitches sounding in combination, and in the Renaissance the concept was expanded to denote three pitches sounding together.
It was not until the publication of Rameau's 'Traité de l'harmonie', in 1722, that any text discussing musical practice made use of the term in the title. The work is however by no means considered the earliest record of theoretical discussion of the topic. This and similar texts tend to survey and codify the musical relationships that were closely linked to the evolution of tonality from the Renaissance, to the late Romanic periods. The underlying principle behind these texts is the notion that harmony sanctions harmoniousness (sounds that 'please') by conforming to certain pre-established compositional principles.
Current dictionary definitions, while attempting to give concise descriptions often highlight the ambiguity of the term in modern use. Such ambiguities tend to arise from either aesthetic considerations (espousing, for example, the view that only "pleasing" concords may be harmonious) or from the point of view of musical texture (distinguishing between harmonic, simultaneously sounding pitches and contrapuntal, successively sounding tones). In the words of Arnold Whitall:
The view that modern tonal harmony in Western music began in about 1600 is commonplace in music theory. This is usually accounted for by the 'replacement' of horizontal (of contrapuntal) writing, common in the music of the Renaissance, with a new emphasis on the 'vertical' element of composed music. Modern theorists, however, tend to see this as an unsatisfactory generalisation. As Carl Dahlhaus puts it:
Descriptions and definitions of harmony and harmonic practice may show bias towards European (or Western) musical traditions. For example, South Asian art music (Hindustani and Karnatak) is frequently cited as placing little emphasis on what is perceived in western practice as conventional 'harmony'; the underlying 'harmonic' foundation for most South Asian music is the drone, a held open fifth (or fourth) that does not alter in pitch throughout the course of a composition. Pitch simultaneity in particular is rarely a major consideration. Nevertheless many other considerations of pitch are relevant to the music, its theory and its structure, such as the complex system of Rāgas, which combines both melodic and modal considerations and codifications within it. So although intricate combinations of pitches sounding simultaneously in Indian classical music do occur they are rarely studied as teleological harmonic or contrapuntal progressions, which is the case with notated Western music. This contrasting emphasis (with regard to Indian music in particular) manifests itself to some extent in the different methods of performance adopted: in Indian Music improvisation takes a major role in the structural framework of a piece, whereas in Western Music improvisation has been uncommon since the end of the 19th century,. Where it does occur in Western music (or has in the past), the improvisation will either embellish pre-notated music or, if not, draws from musical models that have previously been established in notated compositions, and therefore employ familiar harmonic schemes.
There is no doubt, nevertheless, that the emphasis on the precomposed in European art music and the written theory surrounding it shows considerable cultural bias. The Grove Dictionary of Music and Musicians (Oxford University Press) identifies this quite clearly:
Yet the evolution of harmonic practice and language itself, in Western art music, is and was facilitated by this process of prior composition (which permitted the study and analysis by theorists and composers alike of individual pre-constructed works in which pitches (and to some extent rhythms) remained unchanged regardless of the nature of the performance).
Some traditions of music performance, composition, and theory have specific rules of harmony. These rules are often held to be based on natural properties such as Pythagorean tuning's low whole number ratios ("harmoniousness" being inherent in the ratios either perceptually or in themselves) or harmonics and resonances ("harmoniousness" being inherent in the quality of sound), with the allowable pitches and harmonies gaining their beauty or simplicity from their closeness to those properties. While Pythagorean ratios can provide a rough approximation of perceptual harmonicity, they cannot account for cultural factors.
Early Western religious music often features parallel perfect intervals; these intervals would preserve the clarity of the original plainsong. These works were created and performed in cathedrals, and made use of the resonant modes of their respective cathedrals to create harmonies. As polyphony developed, however, the use of parallel intervals was slowly replaced by the English style of consonance that used thirds and sixths. The English style was considered to have a sweeter sound, and was better suited to polyphony in that it offered greater linear flexibility in part-writing. Early music also forbade usage of the tritone, as its dissonance was associated with the devil, and composers often went to considerable lengths, via musica ficta, to avoid using it. In the newer triadic harmonic system, however, the tritone became permissible, as it could form part of a consonant, yet unstable, dominant seventh chord.
Although most harmony comes about as a result of two or more notes being sounded simultaneously, it is possible to strongly imply harmony with only one melodic line through the use of arpeggios or hocket. Many pieces from the baroque period for solo string instruments, such as Bach's Sonatas and partitas for solo violin, convey subtle harmony through inference rather than full chordal structures; see below:
Carl Dahlhaus (1990) distinguishes between coordinate and subordinate harmony. Subordinate harmony is the hierarchical tonality or tonal harmony well known today, while coordinate harmony is the older Medieval and Renaissance tonalité ancienne, "the term is meant to signify that sonorities are linked one after the other without giving rise to the impression of a goal-directed development. A first chord forms a 'progression' with a second chord, and a second with a third. But the earlier chord progression is independent of the later one and vice versa." Coordinate harmony follows direct (adjacent) relationships rather than indirect as in subordinate. Interval cycles create symmetrical harmonies, such as frequently in the music of Alban Berg, George Perle, Arnold Schoenberg, Béla Bartók, and Edgard Varèse's Density 21.5.
Other types of harmony are based upon the intervals used in constructing the chords used in that harmony. Most chords used in western music are based on "tertial" harmony, or chords built with the interval of thirds. In the chord C Major7, C-E is a major third; E-G is a minor third; and G to B is a major third. Other types of harmony consist of quartal harmony and quintal harmony.
The following are common intervals:
|Root||Major Third||Minor third||Fifth|
Therefore, the combination of notes with their specific intervals—a chord—creates harmony. For example, in a C chord, there are three notes: C, E, and G. The note "C" is the root tone, with the notes "E" and "G" providing harmony.
In the musical scale, there are twelve pitches. Each pitch is referred to as a "degree" of the scale. In actuality, there are no names for each degree—there is no real "C" or "E-flat" or "A". Nature did not name the pitches. The only inherent quality that these degrees have is their harmonic relationship to each other. The names A, B, C, D, E, F, and G are insignificant. The intervals, however, are not. Here is an example:
As you can see there, no note always corresponds to a certain degree of the scale. The "root", or 1st-degree note, can be any of the 12 notes of the scale. All the other notes fall into place. So, when C is the root note, the fourth degree is F. But when D is the root note, the fourth degree is G. So while the note names are intransigent, the intervals are not. In layman's terms: a "fourth" (four-step interval) is always a fourth, no matter what the root note is. The great power of this fact is that any song can be played or sung in any key—it will be the same song, as long as the intervals are kept the same.
When the intervals surpass the Octave (12 semitones), these intervals are named as "Extended intervals", which include particularly the 9th, 11th, and 13th Intervals, widely used in Jazz and Blues Music.
Extended Intervals are formed and named as following:
Apart from this categorization, intervals can also be divided into consonant and dissonant. As explained in the following paragraphs, consonant intervals produce a sensation of relax and dissonant intervals a sensation of tension.
The consonant intervals are considered to be the Unison, Octave, Fifth, Fourth and Major and Minor Third. However, harmonically the Fourth interval is considered as a dissonance even though it's the inversion of a Fifth, therefore all the previous intervals are named as Perfect Consonant Intervals while the Fourth is categorized as Imperfect Consonant Interval.
All the other intervals, such as the 7th, 9th, 11th, and 13th are considered Dissonant and require resolution (of the produced tension) and usually preparation (depending on the music style used).
Typically, a dissonant chord (chord with a tension) will "resolve" to a consonant chord. A good harmonization usually sounds pleasant to the ear when there is a balance between the consonant and dissonant sounds. In simple words, that occurs when there is a balance between "tension" and "relax" moments. Because of this reason, usually tensions are 'prepared' and then 'resolved'.
Preparing a tension means to place a series of consonant chords that lead smoothly to the dissonant chord. In this way the composer ensures to build up the tension of the piece smoothly, without disturbing the listener. Once the piece reaches its sub-climax, the listener needs a moment of relaxation to clear up the tension, which is obtained by playing a consonant chord that resolves the tensions of the previous chords. The clearing of this tension usually sounds pleasant to the listener.
Contemporary music has evolved in the way that tensions are less prepared and less structured than in Baroque or Classical periods, thus producing new styles such as Jazz and Blues, where tensions are usually not prepared.